Kim needs to add a 6% saline solution to an IV bag that contains 20 cubic centimeters of 10% saline solution.

How many cubic centimeters (cc) of 6% saline solution must she add to create an 8% solution?

Let 'x' represent the volume of 6% saline solution

Let 'y' represent the volume of 8% saline solution

Form 2 equations.

Eq. 1: 20+x=y

Meaning 20 cm³ + x cm³=y cm³

Eq 2: 0.06x+0.1 (20) = 0.08y

Meaning: 6% of x + 10% of 20 = 8% of y

Use substitution or elimination to solve this linear system. I used substitution.

Sub. Eq. 1 (20+x=y) into Eq. 2 (0.06x+0.1 (20) = 0.08y)

0.06x + 0.1 (20) = 0.08 (20+x)

0.06x+2+1.6=0.08x

-0.02x = - 0.4

x=20

Substitute x=20 into equation 1 (you can also use 2 but in this case equation 1 is simpler)

20+x=y

20+20=y

40=y

To check, substitute x=20 and y=40 into equation 2

0.06x + 0.1 (20) = 0.08y

0.06 (20) + 2 = 0.08 (40)

1.2+2 = 3.2

3.2=3.2

Therefore, Kim would need 20cm³ of 6% saline solution and 40cm³ of 10% saline solution to make 8% solution.